White makes a lot of sense for the Patriots. I put him in my mock for that reason.
Number one, they don't have a third quarterback, but would rather not have to waste a roster spot on one. If they had a guy like White who could be stuffed on the roster as a receiver, and who could also play quarterback, that would be a big deal for them. Sort of like the old days when you had Tupa as your punter. It's a real bonus, and has a big impact on your special teams because you can keep another pure special teamer on your roster (or alternatively it reduces the risk you're taking when you only carry two quarterbacks).
Number two, they don't have a full-time return specialist. That was supposed to be Slater's job, and Slater didn't cut it. If someone like White can take over returning kicks and punts, then you're sparing Welker and Hobbs dangerous duty, and getting more out of that roster spot.
Number three, just imagine defenses trying to cover White in a Wildcat with Moss and Welker out there. Unless you want to single-cover Moss, you leave White with only one guy to beat. The difference between running the wildcat with Ronnie Brown and Ted Ginn on the outside and running it with Pat White and Randy Moss is that with White, you have a guy with a huge NFL-caliber arm who can definitely get it to Moss over the top. You'd end up not having 7-on-7 inside but 7-on-6, because they'd have to roll an extra safety out there.
Come to think of it, I wonder if they might try it with O'Connell. Why not, right?